NO! A SATA power cable is not connected to a video card. A SATA power cable is connected to a SATA device such as a SATA hard disk drive or a SATA optical drive.
A PCI Express power cable is connected to a video card. A video card might require a 6 pin, or 8 pin PCI Express power cable. It just depends on the type of video card.
The power supply that comes with that Apevia pc case is not all that good. You might want to consider buying a case without a pc. Purchase a high quality psu such as Corsair, PC Power & Cooling, or Seasonic. All three brands consistently earn high marks in technical reviews and comparisons. They are high quality units that are very stable and reliable. Those are also the three brands most often recommended by veteran posters at this forum.
A video card is a very important factor in selecting a power supply because a video card typically requires more watts and amps that all of the other components combined. Which video card were you going to install in the system?